Arnold's potentials and quantum catastrophes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F20%3A00522620" target="_blank" >RIV/61389005:_____/20:00522620 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.aop.2019.168050" target="_blank" >https://doi.org/10.1016/j.aop.2019.168050</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aop.2019.168050" target="_blank" >10.1016/j.aop.2019.168050</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Arnold's potentials and quantum catastrophes

Popis výsledku v původním jazyce

In the Thom's approach to the classification of instabilities in one-dimensional classical systems every equilibrium is assigned a local minimum in one of the Arnold's benchmark potentials V-(k)(x) = x(k+1) + c(1)x(k-1) +.... We claim that in quantum theory, due to the tunneling, the genuine catastrophes (in fact, abrupt 'relocalizations' caused by a minor change of parameters) can occur when the number N of the sufficiently high barriers in the Arnold's potential becomes larger than one. A systematic classification of the catastrophes is then offered using the variable mass term h(2)/(2 mu), odd exponents k = 2N + 1 and symmetry assumption V-(k)(x) = V-(k)(-x). The goal is achieved via a symbolic-manipulation-based explicit reparametrization of the couplings c(j). At the not too large N, a surprisingly user-friendly recipe for a systematic determination of parameters of the catastrophes is obtained and discussed.

Název v anglickém jazyce

Arnold's potentials and quantum catastrophes

Popis výsledku anglicky

In the Thom's approach to the classification of instabilities in one-dimensional classical systems every equilibrium is assigned a local minimum in one of the Arnold's benchmark potentials V-(k)(x) = x(k+1) + c(1)x(k-1) +.... We claim that in quantum theory, due to the tunneling, the genuine catastrophes (in fact, abrupt 'relocalizations' caused by a minor change of parameters) can occur when the number N of the sufficiently high barriers in the Arnold's potential becomes larger than one. A systematic classification of the catastrophes is then offered using the variable mass term h(2)/(2 mu), odd exponents k = 2N + 1 and symmetry assumption V-(k)(x) = V-(k)(-x). The goal is achieved via a symbolic-manipulation-based explicit reparametrization of the couplings c(j). At the not too large N, a surprisingly user-friendly recipe for a systematic determination of parameters of the catastrophes is obtained and discussed.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annals of Physics

ISSN

0003-4916

e-ISSN

—

Svazek periodika

413

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

168050

Kód UT WoS článku

000512473400003

EID výsledku v databázi Scopus

2-s2.0-85077236191